$f:\mathbb{R} \rightarrow[0,\infty) $ is a measurable function, if $\int_{-\infty}^{\infty} f(x)=1$, then $\int_{-\infty}^0\frac{1}{1+f(x)}=\infty$

Question

I have to prove this result but I don't know where to start. The hint is, the measure of the set {$x:f(x)<1$} is $\infty$. Can someone help me?